This perfectly formed congruent conflation was uttered by Michael Avenatti on MSNBC (Lawrence O’Donnell). He was referring to Trump’s call to Fox and Friends. It is a mashup of “shoots from the hip” and “speaks off the cuff”, both meaning to speak spontaneously and frankly. “Shoots (one’s) mouth off” (to brag or tell secrets) may also have been in the mix, given the speaker and the subject matter. Interestingly, this is very similar to another malaphor posted previously, “(Trump) shoots from the cuff”, spoken by Megyn Kelly. https://malaphors.com/2015/09/05/trump-shoots-from-the-cuff/
This is one of many political malaphors. You can find many in my book “He Smokes Like a Fish and other Malaphors”, available on Amazon. Just click here: https://www.amazon.com/dp/0692652205
A big thanks to Frank King who spotted another one. He is quickly becoming the Frank King of Malaphors.